The contents in the beakers A and B are 90 ltof milk and 90 ltof water respectively. Now, 30 ltof milk is taken from A and put into B. After thorough mixing, 12 ltof the mixture is taken from B and put into A. Find the percentage of water in beaker A.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Initial Setup
- Beaker A contains 90 liters of milk.
- Beaker B contains 90 liters of water.

### Step 2: Transfer Milk from A to B
- We take 30 liters of milk from Beaker A and add it to Beaker B.
- After this transfer, Beaker A has:
\[ 90 - 30 = 60 \text{ liters of milk} \]
- Beaker B now contains:
\[ 90 \text{ liters of water} + 30 \text{ liters of milk} = 120 \text{ liters of mixture} \]

### Step 3: Composition of the Mixture in Beaker B
- The mixture in Beaker B consists of:
- 30 liters of milk
- 90 liters of water
- The ratio of milk to water in Beaker B is:
\[ \text{Milk:Water} = 30:90 = 1:3 \]

### Step 4: Calculate the Proportions in the Mixture
- The total volume of the mixture in Beaker B is 120 liters.
- The fraction of milk in the mixture is:
\[ \frac{30}{120} = \frac{1}{4} \]
- The fraction of water in the mixture is:
\[ \frac{90}{120} = \frac{3}{4} \]

### Step 5: Transfer Mixture from B to A
- Now, we take 12 liters of this mixture from Beaker B and transfer it back to Beaker A.
- The amount of milk in the 12 liters taken from Beaker B is:
\[ \frac{1}{4} \times 12 = 3 \text{ liters of milk} \]
- The amount of water in the 12 liters taken from Beaker B is:
\[ \frac{3}{4} \times 12 = 9 \text{ liters of water} \]

### Step 6: Update the Contents of Beaker A
- After transferring the 12 liters back to Beaker A:
- Milk in Beaker A becomes:
\[ 60 + 3 = 63 \text{ liters of milk} \]
- Water in Beaker A becomes:
\[ 0 + 9 = 9 \text{ liters of water} \]

### Step 7: Total Volume in Beaker A
- The total volume in Beaker A is:
\[ 63 \text{ liters of milk} + 9 \text{ liters of water} = 72 \text{ liters} \]

### Step 8: Calculate the Percentage of Water in Beaker A
- The percentage of water in Beaker A is calculated as follows:
\[ \text{Percentage of water} = \left( \frac{\text{Volume of water}}{\text{Total volume}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of water} = \left( \frac{9}{72} \right) \times 100 = 12.5\% \]

### Final Answer
The percentage of water in Beaker A is **12.5%**.

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